Approximation of L2-processes by Gaussian processes

M. A. Akcoglu, John R Baxter, D. M. Ha, R. L. Jones

Research output: Contribution to journalArticle

Abstract

Let T be an ergodic transformation of a nonatomic probability space, f an L2-function, and K ≥ 1 an integer. It is shown that there is another L2-function g, such that the joint distribution of T i g, 1 ≤ i ≤ K, is nearly normal, and such that the corresponding inner products (Ti f, Tj f) and (T i g, Tj g) are nearly the same for 1 ≤ i, j ≤ K. This result can be used to give a simpler and more transparent proof of an important special case of an earlier theorem [3], which was a refinement of Bourgain's entropy theorem [9].

Original languageEnglish (US)
Pages (from-to)75-82
Number of pages8
JournalNew York Journal of Mathematics
Volume4
StatePublished - May 21 1998

Keywords

  • Bourgain's entropy theorem
  • Gaussian processes
  • L2-processes

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    Akcoglu, M. A., Baxter, J. R., Ha, D. M., & Jones, R. L. (1998). Approximation of L2-processes by Gaussian processes. New York Journal of Mathematics, 4, 75-82.